Equilibrium Portfolio Research Articles

Real and Financial Sector Interaction Under Liberalization in an Open Developing Economy

A short-run model incorporates instantaneous portfolio equilibrium with macroeconomic flows to clarify the structure of real-financial sector interactions. If equity and foreign exchange markets are introduced in structuralist theories of asset markets in developing countries, the key result that a fall in money supply raises the rate of inflation now holds only under special conditions on partial derivatives. But there is a tendency for interest rates to rise and for fluctuations in asset prices. Fuller integration of asset markets moderates these fluctuations. Outcomes are stable in spite of the generalized complementarity distinguishing equity markets from loan markets. Expectations play a major role. Implications for policy are to link domestic interest rates to foreign, remove artificial barriers to market integration, and stimulate demand as well as supply.

Stochastic differential portfolio games

We study stochastic dynamic investment games in continuous time between two investors (players) who have available two different, but possibly correlated, investment opportunities. There is a single payoff function which depends on both investors’ wealth processes. One player chooses a dynamic portfolio strategy in order to maximize this expected payoff, while his opponent is simultaneously choosing a dynamic portfolio strategy so as to minimize the same quantity. This leads to a stochastic differential game with controlled drift and variance. For the most part, we consider games with payoffs that depend on the achievement of relative performance goals and/or shortfalls. We provide conditions under which a game with a general payoff function has an achievable value, and give an explicit representation for the value and resulting equilibrium portfolio strategies in that case. It is shown that non-perfect correlation is required to rule out trivial solutions. We then use this general result explicitly to solve a variety of specific games. For example, we solve a probability maximizing game, where each investor is trying to maximize the probability of beating the other's return by a given predetermined percentage. We also consider objectives related to the minimization or maximization of the expected time until one investor's return beats the other investor's return by a given percentage. Our results allow a new interpretation of the market price of risk in a Black-Scholes world. Games with discounting are also discussed, as are games of fixed duration related to utility maximization.

Stochastic differential portfolio games

We study stochastic dynamic investment games in continuous time between two investors (players) who have available two different, but possibly correlated, investment opportunities. There is a single payoff function which depends on both investors’ wealth processes. One player chooses a dynamic portfolio strategy in order to maximize this expected payoff, while his opponent is simultaneously choosing a dynamic portfolio strategy so as to minimize the same quantity. This leads to a stochastic differential game with controlled drift and variance. For the most part, we consider games with payoffs that depend on the achievement of relative performance goals and/or shortfalls. We provide conditions under which a game with a general payoff function has an achievable value, and give an explicit representation for the value and resulting equilibrium portfolio strategies in that case. It is shown that non-perfect correlation is required to rule out trivial solutions. We then use this general result explicitly to solve a variety of specific games. For example, we solve a probability maximizing game, where each investor is trying to maximize the probability of beating the other's return by a given predetermined percentage. We also consider objectives related to the minimization or maximization of the expected time until one investor's return beats the other investor's return by a given percentage. Our results allow a new interpretation of the market price of risk in a Black-Scholes world. Games with discounting are also discussed, as are games of fixed duration related to utility maximization.

Stochastic Differential Portfolio Games

We study stochastic dynamic investment games in continuous time between two investors (players) who have available two different, but possibly correlated, investment opportunities. There is a single payoff function which depends on both investors' wealth processes. One chooses a dynamic portfolio strategy in order to maximize this expected payoff while his opponent is simultaneously choosing a dynamic portfolio strategy so as to minimize the same quantity. This leads to a stochastic differential game with controlled drift and variance. For the most part, we consider games with payoffs that depend on the achievement of relative performance goals and/or shortfalls. We provide conditions under which a game with a general payoff function has an achievable value, and give an explicit representation for the value and resulting equilibrium portfolio strategies in that case. It is shown that nonperfect correlation is required to rule out trivial solutions. We then use this general result to explicitly solve a variety of specific games. For example, we solve a probability maximizing game, where each investor is trying to maximize the probability of beating the other's return by a given predetermined percentage. We also consider objectives related to the minimization or maximization of the expected time until one investor's return beats the other investor's return by a given percentage. Our results allow a new interpretation of the market price of risk in a Black-Scholes world. Games with discounting are also discussed as are games of fixed duration related to utility maximization.

Stochastic Dominance, Pareto Optimality, and Equilibrium Asset Pricing

pricing. A factor subspace contains the market portfolio and is such that every marketed contingent claim is second-order stochastically dominated by a claim from the factor subspace. Conditions are given for the existence of equilibrium, and it is shown how APT and CAPM can be interpreted in the framework of the paper. If sufficiently many call options on the market portfolio are traded, then the space spanned by these options can be used as the factor subspace. We consider markets in which a collection of financial assets are traded. The collection may be finite or infinite. Markets are frictionless, and short-sales of assets are permitted. Asset payoffs are random variables which are elements of a space of contingent claims. By forming portfolios of the marketed assets, payoffs in a certain linear subspace of the space of all contingent claims can be attained. We call this subspace a space of marketed claims. We say that a closed subspace of the space of marketed claims is a factor subspace if two conditions are satisfied: first, the market portfolio payoff (i.e. the payoff of an aggregate endowment of portfolios per capita) belongs to this subspace; second, every marketed contingent claim is dominated in the sense of second-order stochastic dominance by some contingent claim in the factor subspace. We demonstrate that for each asset market economy, there is a well-defined minimal factor subspace in the sense that no proper subspace of it can be a factor subspace. If markets are complete, i.e., if a full set of Arrow securities are traded, then the price of any given asset can be expressed in terms of prices of Arrow securities or state prices. Breeden and Litzenberger (1978) have shown that state prices can be replaced by the values of options. Thus in a complete market asset prices are determined either by state prices or call options. It is established in this paper that these ideas and methods are applicable to asset pricing theories even when markets are incomplete. Making use of the argument of second-order stochastic dominance, we show that every constrained Pareto optimal portfolio allocation consists exclusively of portfolios which generate the factor subspace. The same holds for an equilibrium portfolio allocation. Thus, for an economy with a factor subspace, only a partial set of Arrow securities which is large enough to generate the factor subspace is required to price assets. This paper establishes that there exists an equilibrium in which the price of a portfolio equals the price of the dominating portfolio with the same expected return in the factor subspace. Since the dominating

Exchange Rate Dynamics in Dual Exchange Markets

This paper analyzes exchange rate dynamics in dual exchange markets and the impact of unification under various money supply processes and incomplete segmentation between the commercial and financial market by utilizing a two-sector general equilibrium portfolio balance model. It shows that the relationship between the exchange premium and inflation depends not only on inflation elasticity of domestic money demand, but also on the mechanism of domestic credit creation and reserves adjustment. Emphasizing distortionary taxes cumsubsidies created by dual exchange rates, it also shows that unifying dual exchange rates could lead to lower inflation by eliminating distortions. [F31]

Effects of Exchange Rate Changes on Capital Flows

The behaviour of the capital movements with respect to changes in exchange rate has not been studied so far in the Indian literature. The purpose of this paper is, therefore, to study the effects of changes in exchange rate on capital movements by using the Portfolio Equilibrium Model (PEM) and Macroeconomic Model (MEM) developed by Kouri and Porter (1974) and to examine the comparative performance of both these models in this respect. The paper attempts a detailed analysis of the capital flows in India's BoP vis-a-vis exchange rate changes during the period 1960-61 to 1984-85. The results indicate a very strong relationship between trade flows ad short-term capital movements. Another interesting aspect of the results is that income is highly significant in explaining the capital flows in all the cases. In India PEM seems to be more helpful in estimating the short-term and long-term capital movements. The reduced form of MEM does not appear to be useful.

A Bibliography of Finance.

Finance - general decisions under uncertainty economics of information the principal-agent relationship social responsiblity capital markets and securities markets market microstructure intermediation efficiency of securities markets rates of return on securities risk portfolio selection equilibrium prices of risky assets measurement of investment performance valuation of common stocks accounting information and valuation interest rates debt and preferred stock options convertible securities and warrants hedging instruments - futures and forwards capital expenditures cost of capital new securities issues splits and stock dividends cash dividends company financing and capital structure leasing and project finance financial planning working capital mergers and corporate restructuring regulated industries foreign exchange real estate commodity markets and exhaustible resources other speculative markets human capital tax inflation econometrics and statistics.

Uniqueness of Equilibrium in the Classical Capital Asset Pricing Model

General equilibrium in the classical two-period mean-variance capital asset pricing model is not unique. Corresponding to one single set of expectations, utility functions, and an initial wealth distribution, there may be several equilibria, and an asset may have different prices, expected rates of return, and betas in different equilibria. However, any equilibrium portfolio is sustained by a unique price system, and if investors have decreasing risk aversion, then any equilibrium allocation of the risky assets is sustained by a unique price system.

Exchange rate dynamics under gradual portfolio adjustment

This paper generalizes the asset market approach to exchange rate determination by introducing gradual adjustment of asset-holder portfolios. The influence of different speeds of portfolio adjustment on exchange rate dynamics is considered. Asset market models characterized by instantaneous portfolio equilibrium appear as a special case. The dynamics of exchange rate adjustment following an open-market operation are shown to be qualitatively similar to those of the orthodox instantaneous portfolio equilibrium models. Thus, gradual portfolio adjustment does not compromise the qualitative results derived with the help of those models. The speed of portfolio adjustment is however shown to influence the degree of exchange rate volatility. In particular, the phenomenon of exchange rate overshooting depends crucially on the speed of portfolio adjustment.

Real Interest Rates during the Disinflation Process in Developing Countries

This paper addresses a phenomenon often noted in association with programs aimed at stabilizing high rates of inflation: a rise in the ex post real interest rate following implementation of the disinflation strategy. Such increases have been observed in connection with the stopping of European hyperinflations in the 1920s, as well as during the more recent experiences of disinflation in Argentina and Israel. To better understand this behavior, we develop a very general model of interest rate determination in a small open economy with two goods--traded and non-traded--and three assets--money, domestic bonds, and foreign bonds. We show that in partial portfolio equilibrium, a reduction in the fiscal deficit leads to a fall in inflation exceeding the decline in nominal interest rates, so the real interest rate rises; this effect derives from the increase in money demand resulting from the disinflation. In partial goods-market equilibrium, however, a reduction in the fiscal deficit reduces goods demands and lowers the real interest rate. In consequence, the general equilibrium response of the real interest rate to a disinflation program based on fiscal contraction is shown to be indeterminate.The framework described above is used to examine the response of real interest rates to Argentina's disinflation in 1985. We show that the reduction in the fiscal deficit, as well as the government's shift away from money-financing, should have increased real interest rates substantially. However, the imposition of the Austral Plan appears to have exerted an independent effect in reducing interest rates, so that the impact of the program on the real rate of interest was largely neutralized.

Crawling PEG, inflation hedges, and exchange rate dynamics

This paper stresses the effects of currency substitution and speculation on inflation hedges on the relative price of home goods in the two-sector general equilibrium portfolio balance model. Examining the overshooting hypothesis of exchange rates in association with the overshooting phenomenon of price of inflation hedges, it has shown that exchange rate undershooting is plausible with the significant overshooting of the price of inflation hedges when domestic residents hold only domestic money and inflation hedges. However, the impact of currency substitution is strong enough to lead to exchange rate overshooting if the domestic residents have access to foreign currency.

An Intertemporal General Equilibrium Asset Pricing Model: The Case of Diffusion Information

This paper provides sufficient conditions for the equilibrium price system and a vector of exogenously specified state variable processes to form a diffusion process in a pure exchange economy. The conditions involve smoothness of agents' utility functions and certain nice properties of the aggregate endowment process and the dividend processes of traded assets. In place of the dynamic programming, a martingale representation technique is utilized to characterize equilibrium portfolio policies. This technique is useful even when there does not exist a finite dimensional Markov structure in the economy and thus the Markovian stochastic dynamic programming is not applicable. A gents are shown to hold certain hedging mutual funds and the riskless asset. In contrast to earlier results, the market portfolio does not have a special role in hedging, since the markets are dynamically complete. When there exists a finite dimensional Markov system in the economy, the dimension of the hedging demand identified through the Markovian dynamic programming may be much larger than that identified by the martingale method. Copyright 1987 by The Econometric Society.

Generalized concavity of a function in portfolio theory

The analysis of portfolio selection and capital market equilibrium problems involving multivariate lognormal distributions is impeded because this distribution is not closed under addition. To overcome this difficulty it is convenient to use the approximation that this sum is lognormal. Simulation and empirical tests and theoretical results lend support to the appropriateness of the approximation. This paper develops the necessary theory to determine whether such approximating functions are concave or at least quasiconcave and thus their analysis can proceed by standard methods. The characterizations, which involve explicit algebraic criteria related to the parameter values of the random variables and utility function, are evaluated using monthly and yearly stock price data.

Money, Growth and Disequilibrium

The analysis of the trilogy of the title receives an increasing attention in the literature. Malinvaud (1980) analyses the dynamics of a disequilibrium model with a fixed-coefficients technology and an investment function that is common to all disequilibrium regimes. His main conclusion is that only Keynesian equilibria are stable in the long run. Laussel (1980) generalizes this model by relaxing these two assumptions. Several cases appear in his model, but Malinvaud's conclusion is in general vindicated. The present paper shows how a strong wealth effect can stabilize the other types of steady states. However, a complete analysis of the investment function involves a multiplication of the number of disequilibrium regimes. This follows from the role of expectations in investment behaviour. Firms must take into account the various cases of disequilibrium they will have to face before reaching their target capital stock. This reduces the attractiveness of the disequilibrium model as a tool for macroeconomic analysis, because of its exaggerated complexity. Following the tradition of neoclassical growth theory, we sidestep this issue and consider a two-asset-money and capital-world, as Tobin (1961, 1969) advocated. B6hm (1978) has analysed the dynamics of money in a disequilibrium framework, but his model ignores capital accumulation. By contrast, our present model puts the emphasis on portfolio equilibrium, somewhat in the IS-LM tradition (Tobin, 1969). We assume an economy without corporate veil, where profits are wholly received as dividends by households. In Bohm's model these profits are taxed away by the government, while Barro and Grossman (1976), Malinvaud (1977) and Laussel (1980) assume a fixed interest rate. In our model, firms take the real wage rate as given, and determine the rate of interest by paying dividends to their owners. On the asset side, we assume a standard demand-for-money function. As there are only two assets, the demand for capital is defined implicitly by the adding-up conditions (Tobin, 1969), and the investment function could be derived from it, given an initial capital stock. The model is specified in Section I, and its temporary equilibria analysed in Section II. Accumulation of capital is the subject of Section III.

Asset markets and foreign exchange intervention: A model of the Belgo-Luxemburg economic union

In this article a general formulation of government intervention policies in the foreign exchange market is integrated in the framework of an asset market model. The policy reaction function is based on a trade off between exchange rate and reserve stock fluctuations; constant exchange rates and a pure float are derived as limiting cases of the intervention schedule. An exchange rate equation is derived from the short run portfolio equilibrium of the model and is successfully tested using data for the Belgo-Luxemburg Economic Union (1967–1979). Our policy conclusions contrast the European Snake constraints for the Belgian Franc with Artus's findings (IMF Staff Papers XXIII(2), July 1976) for the leading DM.

Insulation Properties of a Two-Tier Exchange Market in a Portfolio Balance Model

When countries peg their currencies to those of their major trading partners, they expose themselves to interest-sensitive and speculative capital flows that can undermine their ability both to maintain their exchange rate and to pursue an independent monetary policy. Some countries, notably France, Italy and the Belgo-Luxembourg Economic Union (BLEU), experimented with two-tier exchange rates in the early 1970s in the hopes of insulating their economies from the effects of international capital flows while at the same time protecting foreign trade from exchange rate fluctuations. France and Italy soon abandoned the experiment, but the BLEU continues to maintain separate exchange markets, with separate exchange rates, for current and capital account transactions. The commercial exchange rate, which relates to the market for current account transactions, is generally pegged by the authorities; the financial exchange rate, determined in the market for capital account transactions, is usually free to fluctuate. 1 This paper investigates how well a two-tier exchange market insulates a small open economy from foreign disturbances, taking into account recent developments in the theory of exchange rate determination. Work by Branson (1977), Dornbusch (1976), and Kouri (1976) suggests that the short-run equilibrium value of the exchange rate is determined, along with interest rates, by demand and supply in the markets for financial assets. This asset market-or portfolio balance-approach to exchange rate determination is particularly well suited to a study of the two-tier exchange market. One can view the financial exchange rate as a relative asset price. It is among the variables that equilibrate asset markets, and it is determined in the short run in those asset markets. Previous theoretical work on the two-tier exchange market has generally been within the Mundellian framework; the financial exchange rate has been treated as equating a flow demand and supply of foreign exchange. The asset market approach has the advantage of carefully distinguishing between stocks and flows. In particular, it treats demands for assets as stock demands that are realized instantaneously so that actual holdings of assets always reflect the desired composition of the portfolio. Disturbances to portfolio equilibrium create immediate stock adjustments as portfolios are rebalanced, causing instantaneous changes in endogenous market-clearing variables. In addition, disturbances alter the rate of accumulation (the flow) of financial assets over time. Portfolio balance models of two-tier exchange rates can be found in Dornbusch (1976) and Decaluwe and Steinherr (1976), but they differ from the one presented here. Dornbusch partitioned the exchange market so that interest income, a current account transaction, was channelled through the financial market. That segmentation yields a different expected rate of return on foreign

Taxation, Portfolio Choice, and Debt-Equity Ratios: A General Equilibrium Model

This paper explores the portfolio behavior of investors differing with respect to both tax rates and risk aversion, emphasizing the role of constraints on individual and firm behavior in ensuring the existence of and characterizing portfolio equilibrium. Under certain conditions on the securities available in the market, which also are necessary for shareholders to be unanimous in supporting firm value maximization, investors will be segmented by tax rate into two groups, one specialized in equity and the other in debt. Though the relative wealths of the two groups determine the aggregate debt-equity ratio, each firm will be indifferent to its financial policy.

LDC participation in international financial markets: Debt and reserves

This paper analyzes LDC borrowing and reserve-holding behavior as part of a general equilibrium portfolio problem. Estimates of LDC debt and reserve demand and credit supply suggest that debt, along with reserves, serves a transactions role. Another finding is that most LDC borrowers are credit constrained. An analysis of LDC export behavior suggests that defaults are likely to be independent, uncorrelated phenomena.

Abstract: Institutional Portfolio Restrictions, Diverse Investor Opportunity Sets, and Securities Market Equilibrium

This paper utilizes a two-parameter model of segmented securities markets to develop equilibrium implications concerning the impact of statutory investment restrictions upon the market prices and allocation of risky securities. The distinguishing feature of the model is the existence of a subset of securities common to the opportunities of all investors and therefore said to “span” the investor population. These common opportunities are shown to permit intersubset security transactions which integrate the various market segments and lead to the following theorem and tendency concerning equilibrium prices and portfolios:Theorem: In the absence of active barriers against short positions, the equilibrium expected return for any security spanning the investor population is an exact linear function of its contribution to total market risk, irrespective of the number of distinct investor segments that may exist.Tendency: The economic characteristics of the equilibrium risky portfolio for any investor, irrespective of the market segment to which he or she may belong, will approximate the characteristics of the market portfolio of all risky assets in the economy in all relevant risk dimensions.